Patterns and Algebra
Teacher
Student Book – Series E
Mathletics
Instant
Workbooks
Copyright ©
Series E – Patterns and Algebra
Contents
Topic 1 –1 Patterns
Section
– Answers
and(p.
functions
1 - 21)
Date completed
• patterns
identifying
and
and
functions_
creating_______________________
patterns_ _________________1
/
/
• equations
skip counting
and__________________________________
equivalence_____________________ 13
/
/
• predicting repeating patterns_____________________
/
/
• predicting growing patterns_ _____________________
/
/
/
/
/
/
• understanding equivalence_______________________
/
/
• not equal to symbol_____________________________
/
/
• greater than and less than_ ______________________
/
/
• balanced equations using + and ×__________________
/
/
• using symbols for unknowns______________________
/
/
• fruit values – solve______________________________
/
/
• mystery snacks – solve_ _________________________
/
/
Section 2 – Assessment with answers (p. 22 - 27)
•
•
•
•
function machines______________________________
patterns and functions_ _______________________ 22
that’s my number – apply________________________
equations and equivalence_____________________ 26
Topic 2 – Equations and equivalence
Section 3 – Outcomes (p. 28 - 30)
Series Author:
Nicola Herringer
Copyright ©
Patterns and functions – identifying and creating patterns
Look around you, can you see a pattern? A pattern is an arrangement of shapes,
numbers or colours formed according to a rule. Patterns are everywhere, you
can find them in nature, art, music and even in dance! Patterns can grow or
repeat depending on the rule
Recognising number patterns is an important part of feeling confident in
maths. In this topic we will look at different number patterns but first let’s look
at shape patterns.
1
Look at these repeating shape patterns. Draw the last two shapes:

a
b





c
2
In these repeating shape patterns, draw the missing shapes:
a
b
3
Complete what comes next in this growing pattern:
Patterns and Algebra
Copyright © 3P Learning Pty Ltd
E
1
SERIES
TOPIC
1
Patterns and functions – identifying and creating patterns
4
Look at these repeating shape patterns. Draw the next 2 shapes:
a
b
c
d
e
5
If the patterns (above) continued, what would the 10th shape be on each row:
a
6
b
c
d
Write your name by putting each letter in
the grid as a repeating pattern. For example,
if your name is Ben, you would write:
1
2
3
4
5
e
1
2
3
4
5
6
7
8
9 10
B
E
N
B
E
N
B
E
N
6
7
8
9
B
10
aWhich letter of your name will be under the letter 32?
b How did you work this out?
Answers will vary.
Patterns and Algebra
Copyright © 3P Learning Pty Ltd
E
1
SERIES
TOPIC
2
Patterns and functions – skip counting
There are many skip counting patterns to discover on a hundred grid.
1
Colour the skip counting pattern on each hundred grid:
bShow the 3s and 6s pattern. Shade
the 3s and circle the 6s.
a Show the 4s pattern.
1
2
3
4
5
6
7
8
9
10
2
3
4
5
6
7
8
9
10
11 12 13 14 15 16 17 18 19 20
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50
41 42 43 44 45 46 47 48 49 50
51 52 53 54 55 56 57 58 59 60
51 52 53 54 55 56 57 58 59 60
61 62 63 64 65 66 67 68 69 70
61 62 63 64 65 66 67 68 69 70
71 72 73 74 75 76 77 78 79 80
71 72 73 74 75 76 77 78 79 80
81 82 83 84 85 86 87 88 89 90
81 82 83 84 85 86 87 88 89 90
91 92 93 94 95 96 97 98 99 100
91 92 93 94 95 96 97 98 99 100
dShade the 9s pattern, then put a
circle around all the numbers 5 less
than numbers ending in 9.
c Show the 11s pattern.
1
2
1
2
3
4
5
6
7
8
9
10
1
2
3
4
5
6
7
8
9
10
11 12 13 14 15 16 17 18 19 20
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50
41 42 43 44 45 46 47 48 49 50
51 52 53 54 55 56 57 58 59 60
51 52 53 54 55 56 57 58 59 60
61 62 63 64 65 66 67 68 69 70
61 62 63 64 65 66 67 68 69 70
71 72 73 74 75 76 77 78 79 80
71 72 73 74 75 76 77 78 79 80
81 82 83 84 85 86 87 88 89 90
81 82 83 84 85 86 87 88 89 90
91 92 93 94 95 96 97 98 99 100
91 92 93 94 95 96 97 98 99 100
Complete these number patterns by looking for skip counting patterns.
a
6
12
18
24
30
36
42
48
b
9
18
27
36
45
54
63
72
c
32
28
24
20
16
12
8
4
Patterns and Algebra
Copyright © 3P Learning Pty Ltd
E
1
SERIES
TOPIC
3
Patterns and functions – skip counting
3
Colour the skip counting
pattern for 3s up to 30.
If you kept going on a complete
hundred grid, would 52 be
coloured in?
1
2
3
4
5
6
7
8
9
10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
How can you tell without using a whole hundred grid?
No,
because 52 is not a multiple of 3.
____________________________________________________________________
4
Only 3 numbers are shaded in each of the skip counting patterns below. Work out
the pattern and complete the shading:
a
1
2
3
4
5
6
8
9
b
10
1
2
3
4
5
6
8
7
9
10
11 12 13 14 15 16 17 18 19 20
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50
41 42 43 44 45 46 47 48 49 50
51 52 53 54 55 56 57 58 59 60
51 52 53 54 55 56 57 58 59 60
61 62 63 64 65 66 67 68 69 70
61 62 63 64 65 66 67 68 69 70
71 72 73 74 75 76 77 78 79 80
71 72 73 74 75 76 77 78 79 80
81 82 83 84 85 86 87 88 89 90
81 82 83 84 85 86 87 88 89 90
91 92 93 94 95 96 97 98 99 100
91 92 93 94 95 96 97 98 99 100
This shows a skip
counting pattern of:
5
7
This shows a skip
counting pattern of:
4s
8s
Shade these sequences on the hundred grid:
Sequence 1: start at 1 and show
a skip counting pattern of 11.
Sequence 2: start at 1 and show
a skip counting pattern of 9.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99 100
Patterns and Algebra
Copyright © 3P Learning Pty Ltd
E
1
SERIES
TOPIC
4
Patterns and functions – completing and describing patterns
So far we have looked at skip counting patterns that begin at zero.
Here is a skip counting pattern of 5s that begins at 7.
This pattern starts at 7.
7
The rule is: Add 5.
1
2
+5
17
+5
22
27
+5
+5
Continue the pattern from the starting number:
a
Add 10
11
21
31
41
51
61
71
81
b
Add 5
55
60
65
70
75
80
85
90
c
Subtract 4
40
36
32
28
24
20
16
12
Practise counting backwards by 10 and 100.
Backwards by 10:
3
12
Backwards by 100:
a
112
102
92
82
72
a
673
573
473
373
273
b
219
209
199
189
179
b
798
698
598
498
398
c
583
573
563
553
543
c
1 010 910
810
710
610
Look carefully at these number pattern grids. There are 4 rules: across, down, and
along each diagonal.
a
15
16
17
18
25
26
27
35
36
45
46
b
32
35
38
41
28
38
41
44
47
37
38
44
47
50
53
47
48
50
53
56
59
Patterns and Algebra
Copyright © 3P Learning Pty Ltd
E
1
SERIES
TOPIC
5
Patterns and functions – completing and describing patterns
4
Figure out the missing numbers in each pattern and write the rule.
a
72
63
54
45
36
b
27
–9
Rule: _________________________
c
44
49
54
64
59
81
73
65
57
49
41
–8
Rule: _________________________
d
69
+5
Rule: _________________________
28
35
42
49
56
63
+7
Rule: _________________________
Some number patterns can be formed with 2 operations each time.
For example:
2
×2+3
×2+3
7
17
×2+3
37
The rule is to multiply by 2 and add 3 each time.
5
Complete these number patterns, by following the rules written in the diamond
shapes. Describe the rule underneath.
3
+5x2
16
+5x2
42
+5x2
94
to add 5 and multiply by 2 each time.
The rule is____________________________________________________________
6
Roll a die to make the starting number. Continue the sequence by following the rule:
a
Rule: + 4 × 2
b
Rule: + 1 × 3
c
Rule: + 3 × 2
Answers will vary.
Patterns and Algebra
Copyright © 3P Learning Pty Ltd
E
1
SERIES
TOPIC
6
Patterns and functions – predicting repeating patterns
When we use number patterns in tables, it can help us to predict what comes
next. Look at the table below and how we can use it to predict the total number
of sweets needed for any number of children at a party.
This table shows us that 1 sweet bag contains 8 sweets and 2 bags contain 16
sweets. We can see that the rule for the pattern is to multiply the top row by 8
to get the bottom row each time.
Number of sweet bags
1
2
3
4
5
10
Number of sweets
8
16
24
32
40
80
×8
To find out how many sweets are in 10 bags, we don’t need to extend the table,
we can just apply the rule.
10 × 8 = 80. So, 10 bags contain 80 sweets. This helps us plan how many
sweets are needed for a party.
1
Complete the table for each problem:
aTom receives $5 a week pocket money as long as he does all his chores. How
much pocket money does Tom get after 10 weeks?
Weeks
1
2
3
4
5
10
Pocket money
5
10
15
20
25
50
bA flower has 7 petals. How many petals are there in a bunch of 10 flowers?
Flowers
1
2
3
4
5
10
Number of petals
7
14
21
28
35
70
cA flag has 6 stars. How many stars are there on 10 flags?
Flags
1
2
3
4
5
10
Number of stars
6
12
18
24
30
60
dAt a pizza party, each person eats 3 pieces of pizza. How many pieces of pizza do
10 people eat?
Guests
1
2
3
4
5
10
Pizza pieces
3
6
9
12
15
30
Patterns and Algebra
Copyright © 3P Learning Pty Ltd
E
1
SERIES
TOPIC
7
Patterns and functions – predicting repeating patterns
2
Each of these kids wrote the first 3 numbers of a skip counting pattern of 6,
starting at different numbers. Each kid’s sequence goes down the column.
Imagine the sequence continues.
Mel
Brianna
Brad
Gen
Jo
Kate
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
Kate
a Who had the number 42 in their column?_ _______________________________
Brianna
b Who had the number 50 in their column?_ _______________________________
3
Look at each pattern of shapes and complete the table below:
Repeat section
1
2
3
4
5
10
Number of circles
2
4
6
8
10
20
Number of triangles
1
2
3
4
5
10
aShow what this entire sequence would look like with 10 repeat sections:
Look for the section that
repeats. What is it made
up of? This is the rule.
Patterns and Algebra
Copyright © 3P Learning Pty Ltd
E
1
SERIES
TOPIC
8
Patterns and functions – predicting growing patterns
Number patterns in tables can help us with problems like this. Mia is making
this sequence of shapes with matchsticks and wants to know how many she
will need for 10 shapes.
Shape 1
Shape 2
Shape 3
Shape number
1
2
3
4
5
10
Number of matchsticks
3
6
9
12
15
30
×3
To find out how many matchsticks are needed for 10 triangles, we don’t need
to extend the table, we can just apply the function rule:
Number of matchsticks = Shape number × 3
1
Complete the table for each sequence of matchstick shapes and find the number
of matchsticks needed for the 10th shape.
a
b
c
Shape 1
Shape 2
Shape 3
Shape number
1
2
3
4
5
10
Number of matchsticks
4
8
12
16
20
40
Shape 1
Shape 2
Shape 3
Shape number
1
2
3
4
5
10
Number of matchsticks
6
12
18
24
30
60
Shape 1
Shape 2
Shape 3
Shape number
1
2
3
4
5
10
Number of matchsticks
7
14
21
28
35
70
Patterns and Algebra
Copyright © 3P Learning Pty Ltd
E
1
SERIES
TOPIC
9
Patterns and functions – predicting growing patterns
2
Look at these growing patterns. Complete the table and follow the rule to draw
Picture 5:
a
Picture 1
Picture 2
l
ll
l
Picture 4
Picture 5
l
l
lll
l
l
l
llll
l
l
l
l
lllll
Picture number
1
2
3
4
5
Number of dots
1
3
5
7
9
Rule
b
Picture 3
Picture number × 2 – 1 = Number of dots
Picture 1
Picture 2
Picture
number
1
2
3
4
5
Number of
squares
4
6
8
10
12
Rule
Picture 3
Picture 4
Picture 5
Picture number × 2 + 2 = Number of squares
How many squares will Picture 8 have?
8 × 2 + 2 = 18 squares
Patterns and Algebra
Copyright © 3P Learning Pty Ltd
E
1
SERIES
TOPIC
10
Patterns and functions – function machines
This is a function machine.
IN
Numbers go in, have the rule
applied, and come out again.
2
OUT
RULE:
6
×3
8
24
10
1
Look carefully at the numbers going in these function machines and the numbers
coming out. What is the rule?
a
b
IN
5
8
RULE:
×3
9
2
OUT
15
IN
4
24
7
27
9
OUT
24
RULE:
×6
42
54
What numbers will come out of these function machines?
b
a
IN
3
4
RULE:
×8
7
3
30
OUT
24
IN
24
32
48
56
72
OUT
RULE:
3
÷8
6
9
What numbers go in to these number function machines?
a
b
IN
46
62
122
RULE:
– 10
OUT
36
IN
68
52
277
112
112
Patterns and Algebra
Copyright © 3P Learning Pty Ltd
OUT
78
RULE:
+ 10
287
122
E
1
SERIES
TOPIC
11
That’s my number!
Getting
ready
What
to do
apply
This is a game for 2 players. You will need some
transparent counters each in 2 different colours and
2 dice.
copy
Player 1 rolls 2 dice. The first die shows the starting number and
the second die shows the skip counting pattern. Player 1 writes
down the first 4 numbers of their sequence.
For example, if Player 1 rolls a 2 and a 6, the starting number is 2
and the rule is + 6. So Player 1 writes 2, 8, 14, 20 and chooses one
of these numbers to cover with their counter.
Player 2 has their turn, following the same steps as above. They
choose one number to cover with their counter. If the number is
already covered, they can’t put down a counter. The winner is the
first player to have their counters in a group of 4 (2 × 2).
1
2
3
4
5
6
7
8
9
10
7
8
9
10
15
16
17
18
19
20
21
22
23
24
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
1
2
3
4
Patterns and Algebra
Copyright © 3P Learning Pty Ltd
E
1
SERIES
TOPIC
12
Equations and equivalence – understanding equivalence
Look at these balanced scales.
On one side there is the sum 4 + 3 and
on the other side there is a total of
7 triangles. This makes sense because it
shows the equation 4 + 3 = 7.
4 + 3
Equation is another word for a sum. With
equations, both sides must be equal.
1
4 + 3 = 7
Balance each set of scales by writing a number in the box that is equivalent to the
total number of shapes. Then write the matching equation.
5 +
4
5
+
4
=
9
5
+
3
=
8
a
5 +
3
b
2
Balance each set of scales by writing a number in the box. Then write the
matching equation.
30
+ 55
85
30
+
55
=
85
45 +
55
100
45
+
55
=
100
a
b
Patterns and Algebra
Copyright © 3P Learning Pty Ltd
E
2
SERIES
TOPIC
13
Equations and equivalence – not equal to symbol
When two sides of an equation are not balanced,
it means that they are not equal. To show that
an equation is not equal, we use the not equals
symbol like this:
1
+
12
≠
9
20
Write numbers in each box to show equations that are not balanced:
a
50
b
70
45
65
+
65
200
+
50
70
≠
≠
200
45
Answers
will vary.
c
d
35
30
185
160
≠
185
35
+
+
30
Answers
will vary.
2
≠
160
Answers
will vary.
Complete the equations below by using only the numbers in the cards.
Look carefully to see whether it is an = or ≠ symbol.
20
a
15
+
35
=
50
15
35
b
or
c
20
+
15
=
35
d
or
Patterns and Algebra
Copyright © 3P Learning Pty Ltd
20
+
15
≠
50
20
+
35
≠
50
15
+
35
≠
35
20
+
35
≠
35
E
2
SERIES
TOPIC
14
Equations and equivalence – greater than and less than
When two sides of an equation are not balanced, one side is greater than the
other. We can show this with greater than (>) and less than (<) symbols like this:
12
25
14
15
30
+
12
1
<
14
30
+
15
13
>
13
25
Complete the equations below by using only the numbers in the cards. Look
carefully to see whether it is an > or < symbol. The first one has been done for you.
a
18
22
b
50
35
25
50
18 + 22
50
35 + 25
50
18
c
+
22
<
78
32
100
50
35
or
or
50
50
d
100
+
25
>
107
83
200
+
+
25
35
2
78
100
100
+
+
+
35
25
107 + 83
78 + 32
or
or
50
>
>
200
32
32
78
>
>
>
107
100
78
32
+
<
83
200
Alex is older than Gilly but younger than Taylor. Their ages could be described as:
16 > 12 > 9
How old is each person?
12
Alex is ______
9
Gilly is ______
Patterns and Algebra
Copyright © 3P Learning Pty Ltd
16
Taylor is ______
E
2
SERIES
TOPIC
15
Equations and equivalence – greater than and less than
3
Complete the number sentences below by writing numbers in the blank boxes:
Answers will vary.
a
4
38
+
>
100
b
29
+
+
257
d
500
<
1 000
f
+
<
h
+
<
c
>
e
+
>
g
+
>
243
<
460
100
+
1 000
Sam and Will’s mother is
When you add these amounts, look for
trying to work out how much
bonds to $1. For example:
to budget for her children’s
$1.40 + $1.60 = (40c + 60c) + $1 + $1 = $3
daily lunch orders. She is
wondering if $50 is enough for
both Sam and Will. Add up the cost of each child’s lunch order
for the week and then complete a matching number sentence.
Sam’s lunch
orders
Monday
Tuesday
Wednesday
Thursday
Friday
$4.60
$5.40
$7.30
$3.70
$6
Will’s lunch
orders
Monday
Tuesday
Wednesday
Thursday
Friday
$5.20
$3.80
$5.90
$6.10
$5
+
$27
Sam’s total
$26
>
$50
Will’s total
Patterns and Algebra
Copyright © 3P Learning Pty Ltd
E
2
SERIES
TOPIC
16
Equations and equivalence – balanced equations using
+ and ×
There are 2 different equations we could write for one set of balanced scales.
8
1
8
8
24
8
+
8
+
8
=
3
×
8
=
24
24
Work out the values of the symbols in each problem:
a
b
9
9
9
9
9
7
7
7
7
7
7
45
5
×
9
=
45
42
6
×
7
=
42
63
7
×
9
=
63
42
6
×
7
=
42
c
d
Patterns and Algebra
Copyright © 3P Learning Pty Ltd
E
2
SERIES
TOPIC
17
Equations and equivalence – balanced equations using
+ and ×
2
Find the values of these symbols:
a If
is 5, what is the value of
?
2
b If
is 8, what is the value of
5
=
5
=
2
=
6
=
4
×
2
×
4
×
12
=
12
×
2
=
2
?
3
3
×
×
8
Find the values of both symbols from the clues:
a If both sides are equal to 36, what is the value of each symbol?
2
×
18
=
18
=
3
b If both sides are equal to 10, what is the value of each symbol?
2
Patterns and Algebra
Copyright © 3P Learning Pty Ltd
×
5
=
5
=
5
E
2
SERIES
TOPIC
18
Equations and equivalence – using symbols for unknowns
1
Write an equation for these word problems. Write an equation using a
unknown number.
s for the
aBec collects stickers. She has 48 bumper stickers, 12 glitter stickers and 15 smiley
face stickers. How many stickers does Bec have in her collection?
+
48
12
+
15
=
s=
s
75
bCharlie saved $5 a week of his pocket money over 8 weeks but then spent $15.
How much did Charlie have at the end of 8 weeks?
$5 × 8 – $15=
s=
s
$25
c5 000 people are spectators at a football match. 2 700 are there to support Team A
while the rest are there to support Team B. How many spectators support Team B?
5 000 – 2 700=
2
s=
s
2 300
In this triangle, the numbers on the sides are the totals.
So 10 +
25
30
15
= 30
Work out the value of the other symbols:
10
= 20
Patterns and Algebra
Copyright © 3P Learning Pty Ltd

=
5
E
2
SERIES
TOPIC
19
Fruit values
What
to do
solve
Work out the value of each type of fruit:
37
=
11
=
15
=
9
=
10
=
2
=
11
=
16
=
11
=
1
45
33
35
39
41
14
33
22
15
23
31
18
38
33
48
13
28
Patterns and Algebra
Copyright © 3P Learning Pty Ltd
E
2
SERIES
TOPIC
20
Mystery snacks
What
to do
solve
Work out what is the snack box from the clues.
Clue 1
Clue 2
Hint: Keep the scale
balanced by adding
Crunchy O to each side
in Clue 2. Then work out
what else 2 packets of
chips is equal to. From
there, you can work out
your answer.
Patterns and Algebra
Copyright © 3P Learning Pty Ltd
E
2
SERIES
TOPIC
21
Patterns and functions
1
Name___________________
Each child has 4 buttons on their school shirt. Complete the table to show how
many buttons different amounts of children have.
Number of children
1
Number of buttons
4
2
3
4
5
10
a How many buttons do 20 children have?
b How did you work this out?
__________________________________________________________________
2
Complete these function machines.
a
b
IN
6
7
RULE:
OUT
IN
OUT
57
RULE:
×5
+ 10
34
9
3
98
Complete the table for each sequence of matchstick shapes and find the number
of matchsticks needed for 10th shape:
Shape 1
Shape 2
Shape 3
Shape number
1
Number of matchsticks
6
2
Skills
3
4
Not yet
5
Kind of
10
Got it
ompletes a shape or number pattern by following
• C
a function rule
an write a rule to describe input and output
• C
relationships
Series E Topic 1 Assessment
Copyright © 3P Learning Pty Ltd
22
Patterns and functions
1
Name___________________
Each child has 4 buttons on their school shirt. Complete the table to show how
many buttons different amounts of children have.
Number of children
1
2
3
4
5
10
Number of buttons
4
8
12
16
20
80
a How many buttons do 20 children have?
80
b How did you work this out?
Multiplied the number of children by 4.
__________________________________________________________________
2
Complete these function machines.
a
b
IN
6
7
RULE:
OUT
IN
30
47
35
24
45
88
×5
9
3
OUT
57
RULE:
+ 10
34
98
Complete the table for each sequence of matchstick shapes and find the number
of matchsticks needed for 10th shape:
Shape 1
Shape 2
Shape 3
Shape number
1
2
3
4
5
10
Number of matchsticks
6
12
18
24
30
60
Skills
Not yet
Kind of
Got it
ompletes a shape or number pattern by following
• C
a function rule
an write a rule to describe input and output
• C
relationships
Series E Topic 1 Assessment
Copyright © 3P Learning Pty Ltd
23
Patterns and functions
4
Complete these number patterns by looking for skip counting patterns:
a
7
28
72
b
5
Name___________________
35
54
36
Colour the skip counting pattern for 4s up to 30.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
aIf you kept going on a
complete hundred grid,
would 54 be coloured in?
Yes
/
No
bHow can you tell without using a whole hundred grid?
––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––
6
Figure out the missing numbers each pattern and write the rule:
a
56
49
35
b
28
Rule: _________________________
7
30
36
42
Rule: _________________________
Complete a number sequence for each rule:
Rules
Sequences
× 2 + 1
2
× 2 – 1
2
× 3 – 1
2
Skills
Not yet
Kind of
Got it
• Completes a skip counting pattern
• Completes a number pattern and write the rule in words
• Completes a number pattern with 2 operations
Series E Topic 1 Assessment
Copyright © 3P Learning Pty Ltd
24
Patterns and functions
4
5
Name___________________
Complete these number patterns by looking for skip counting patterns:
a
7
14
21
28
35
42
49
56
b
81
72
63
54
45
36
27
18
Colour the skip counting pattern for 4s up to 30.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
aIf you kept going on a
complete hundred grid,
would 54 be coloured in?
Yes
/
No
bHow can you tell without using a whole hundred grid?
54 is not in the 4 times table.
––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––
6
Figure out the missing numbers each pattern and write the rule:
a
56
49
42
35
28
b
21
–7
Rule: _________________________
7
30
36
42
48
54
60
+6
Rule: _________________________
Complete a number sequence for each rule:
Rules
Sequences
× 2 + 1
2
5
11
23
47
95
× 2 – 1
2
3
5
9
17
33
× 3 – 1
2
5
14
41
122
365
Skills
Not yet
Kind of
Got it
• Completes a skip counting pattern
• Completes a number pattern and write the rule in words
• Completes a number pattern with 2 operations
Series E Topic 1 Assessment
Copyright © 3P Learning Pty Ltd
25
Equations and equivalence
1
Complete this equation to show it on the balanced scales:
30 +
2
+
100
=
Complete the number sentences below by writing numbers in the blank boxes:
a
3
Name___________________
25
+
>
100
b
29
+
<
100
Find the value of the symbol:
a
42
=
bMia saved $9 of her pocket money each week over 6 weeks but then spent $15.
How much did she have at the end of 6 weeks?
Write an equation using a symbol to represent the unknown and show your
working in the space below:
Skills
Not yet
Kind of
Got it
• Recognises that equals sign means equivalence
• Recognises the greater than and less than symbol
• Finds the value of a symbol
Series E Topic 2 Assessment
Copyright © 3P Learning Pty Ltd
26
Equations and equivalence
1
Complete this equation to show it on the balanced scales:
30 +
2
Name___________________
+
30
100
70
70
=
100
Complete the number sentences below by writing numbers in the blank boxes:
Answers will vary.
a
3
25
+
>
100
b
+
29
<
100
Find the value of the symbol:
a
=
42
7
bMia saved $9 of her pocket money each week over 6 weeks but then spent $15.
How much did she have at the end of 6 weeks?
Write an equation using a symbol to represent the unknown and show your
working in the space below:
($9 × 6) – $15 =
$54 – $15 = $39
= $39
* Choice of symbol will vary.
Skills
Not yet
Kind of
Got it
• Recognises that equals sign means equivalence
• Recognises the greater than and less than symbol
• Finds the value of a symbol
Series E Topic 2 Assessment
Copyright © 3P Learning Pty Ltd
27
Series E – Patterns and Algebra
Topic 1
Patterns and functions
Topic 2
Equations and equivalence
NSW
PAS2.1 – Generates, describes and records
number patterns using a variety of strategies
and completes simple number sentences by
calculating missing values
• identifying and describing patterns when
counting forwards or backwards by threes,
fours, sixes, sevens, eights or nines
• creating, with materials or a calculator, a
variety of patterns using whole numbers
• finding a higher term in a number pattern
given the first five terms e.g. determine the
10th term given a number pattern beginning
with 4, 8, 12, 16, 20, …
• working through a process of building a
simple geometric pattern involving multiples,
completing a table of values, and describing
the pattern in words
PAS2.1 – Generates, describes and records
number patterns using a variety of strategies
and completes simple number sentences by
calculating missing values
• forming arrays using materials to
demonstrate multiplication patterns and
relationships
• completing number sentences involving one
operation by calculating missing values
• applying the associative property of addition
and multiplication to aid mental computation
e.g. 2 + 3 + 8 = 2 + 8 + 3, 2 × 3 × 5 = 2 × 5 × 3
• using the equals sign to record equivalent
number relationships and to mean ‘is the
same as’ rather than as an indication to
perform an operation e.g. 4 × 3 = 6 × 2
VIC
Number VELS – Level 3
• at Level 3, students recognise the
mathematical structure of problems and
use appropriate strategies (for example,
recognition of sameness, difference and
repetition) to find solutions
• students use calculators to explore number
patterns and check the accuracy of estimations
Number VELS – Level 3
• at Level 3, students recognise the
mathematical structure of problems and
use appropriate strategies (for example,
recognition of sameness, difference and
repetition) to find solutions
PA 3.1 – Students create and continue number
patterns, identify, describe and represent
relationships between two quantities and
use backtracking to reverse any one of the
four operations
• input → output (function machines)
• number
– rules based on previous term
– calculators (whole and decimal numbers
involving any operations)
– missing term
– non-patterns or patterns with errors
– rules based on the position of terms
(one operation only)
• representations of relationships
– rules, tables, graphs
PA 3.2 – Students represent and describe
equivalence in equations that involve
combinations of multiplication and division or
addition and subtraction
• number
– rules based on previous term
– calculators (whole and decimal numbers
involving any operations)
– missing term
– non-patterns or patterns with errors
– rules based on the position of terms
(one operation only)
• equations (number sentences)
• symbols
– equals (=)
– does not equal (≠)
– greater than (>)
– less than (<)
– for unknowns (shapes, boxes, question
marks, spaces, lines)
Region
QLD
Series E Outcomes
Copyright © 3P Learning Pty Ltd
28
Series E – Patterns and Algebra
Region
Topic 1
Patterns and functions
Topic 2
Equations and equivalence
SA
2.9 – Searches for, represents and analyses different forms of spatial and numerical patterns, and
relates these to everyday life
2.10 – Represents and communicates patterns with everyday and mathematical language,
including symbols, sketches, materials, number lines and graphs
• represents and analyses different forms of patterns of number, shape and measurement drawn
from everyday life
• represents spatial patterns with tables, drawings and symbols
WA
N 6a.2
• reads, writes, says and counts with whole numbers to beyond 100, using them to compare
collection sizes and describe order
A 2 Algebra
• complete either addition, subtraction,
multiplication and division number sentences
by calculating a missing number
e.g. ___ + 8 = 17, 5 + 2 = __ + 3
• use the equal sign to mean ‘is the same as’,
e.g. 4 + 3 = 2 + 5
NT
A 2 Algebra
• recognise and continue physical patterns
formed by repeatedly adding or subtracting a
predictably increasing or decreasing number
of elements
• express patterns as a number sequence
• generate patterns and number sequences
given a description or set of instructions
• continue and complete number sequence
patterns involving repeated addition
or subtraction
• complete equations involving simple addition
or subtraction where one of the elements
(addend, minuend or subtrahend) is missing
• use words and tables to record relationships
between pairs of numbers
18.LC.9 – inverse and equivalence relationships,
including how inverse operations enable
them to work out related number facts and
solve unknown elements of simple equations
involving addition and subtraction
18.LC.11 – equations (number sentences and
models to represent mathematical problems
and situations based around a single operation
ACT
18.LC.1 – patterns in number and space (e.g.
multiple copies of shapes tessellation) and the
role that position plays in patterns
18.LC.4 – basic transformations (flips, slides and
turns) of shapes and description of the changes
that occur
18.LC.16 – represent and interpret patterns
in number and space, identify the rules that
describe the pattern, work out further elements
and use materials to model and continue
spatial patterns
18.LC.21 – recognise and describe relationships
and represent them using concrete materials,
drawings, lists, tables and some mathematical
symbols
18.LC.22 – analyse simple relationships and
make predictions based on the information
they have
Series E Outcomes
Copyright © 3P Learning Pty Ltd
29
Series E – Patterns and Algebra
Region
TAS
Topic 1
Patterns and functions
Topic 2
Equations and equivalence
Standards 2 - 3, Stages 4 - 8
• using objects, pictures and other symbols to
represent problem situations
• using number to describe patterns e.g. ‘My
pattern is a counting by 6 pattern’, or ‘my
pattern doubles each time’
• making and extending more sophisticated
patterns with materials and with numbers
e.g. using the constant function on a basic
calculator to count by a given number and
explore patterns or finding out what happens
when we keep doubling numbers
• exploring growth patterns in table form
• creating and follow sequences of actions and
instructions e.g. follow a set of instructions,
follow a tourist guide, create ‘think of a
number’ problems or a set of rules for
a dice game
• making predictions based on growth patterns
e.g. simple match stick or block patterns
• investigating patterns in the number system
e.g. adding ten to a number, odd and
even number investigations, patterns in
multiplication and division
Standards 2 - 3, Stages 4 - 8
• using equivalence to solve simple equations
with unknowns e.g. 5 + 4 = + 2
• exploring situations where inverse operations
can be applied and describe how inverse
operations apply to other situations and
problems e.g. interpret 13 = + 8 as a
subtraction situation, use a 4 by 3 array
to work out associated multiplication and
division problems
• identifying and describing relationships, such
as inverses and equivalence in a variety of
ways e.g. using balances to show that 14 + 8
can be changed to 12 + 10 without affecting
the equivalence
• identifying and describing relationships, such
as inverses and equivalence in a variety of
ways e.g. using balances to show that 14 + 8
can be changed to 12 + 10 without affecting
the equivalence
Series E Outcomes
Copyright © 3P Learning Pty Ltd
30